In another development, much attention has been paid to the multi-mode coherent states, Gerry et al. [1]} propose a method for generating ECSs of a two-mode field. Moreover, ones have studied the optimal quantum information processing via GHZ-type [2]} and W-type ECSs [3]}. Jeong's group [2]} present the generation of GHZ-type ECSs using beam splitters (BSs) with a single-mode CSS and demonstrate Bell inequality violations for GHZtype ECSs. Some theoretical schemes have been proposed to generate the GHZ-type ECS in cavity fields [5]}, [6]}. Kuang's group [7]}, [8]} propose single-mode and two-mode excite ECSs and their generation via cavity QED. The optical generation of excited ECSs is also investigated by using the BSs and the type-I beta-barium borate (BBO) crystal [9]}, [10]}. Furthermore, the photon-added coherent state (PACS) was first proposed by Agarwal and Tara [11]}, they
presented a hybrid non-classical state called a PACs which exhibits an intermediate property between a classical coherent state (CS) and a purely quantum Fock state (FS) [11]}. More recently, by using a type-I BB) crystal, a single photon detector (SPD) and a balanced homodyne detector, Zavatta et al. experimentally created a single-photon-added coherent state (SPACS) which allowed them to first visualize the classical-to quantum transition process [13]}. In the other hand, the authors [14]} try to present a general formalism for the construction of deformed photon-added nonlinear coherent states (DPANCSs), which in special case lead to the well-known PACS. Recently, [15]} introduced a new kind of photon-added entangled coherent states (PA-ECSs), by performing repeatedly an f-deformed photon-addition (DPA) operation, on each mode of the entangled coherent states (ECSs). By choosing a particular deformation function, as a result, they study how the entanglement properties can be enhanced by DPA operation. Furthermore, their findings indicate that there is a family of coherent amplitudes \(\left|\alpha \right|\)  for which the two-mode DPA operation preserves the maximal entanglement of the odd ECSs while the non-deformed photon-addition operation suppresses it. In the other study, Mojaveri et al. want to see how adding photons to two-qutrit entangled states affects them. They give a general study of non-classical features including photon statistics and entanglement for this purpose, with a focus on the control role of the shift parameter in these states [16]}.
